1. Technical Field
The present disclosure relates to the detection of a threshold crossing instant by an electrical signal, by means of an electronic device. In particular, the disclosure relates to a method and a device capable of detecting, with a high temporal accuracy, a threshold crossing instant of an electrical signal converted in digital form.
2. Description of the Related Art
In several electronic systems, it is essential to detect an instant at which an electrical signal crosses a threshold level, or threshold.
The threshold crossing may be representative, in different application scopes, of different events: for example, it may be associated to a change in the digital logical level, or it may discriminate a condition of signal “absence” (off) from a condition of signal “presence” (on), or vice versa.
In particular, for an electrical signal having a monotonic leading or trailing edge, the crossing instant of a threshold may represent a “time of arrival” (TOA) or a “time of transmission” (TOT) of the signal.
Such definitions of TOA and TOT are well known in the considered technical field, especially in the context of systems for which the time of arrival or transmission of a signal is essential: this is true, for example, in reception and transmission systems for radar signals, or in localization (such as the GPS system) or synchronization systems.
It should be noted that, in such systems, it is essential for the detection to be temporally accurate, that is, it should occur in an instant having a fixed delay, known with a high accuracy and steady, relative to the instant at which the signal is physically received, for example by an analog receiver. In other words, the requirements of a system for detecting the time of arrival relate not much to the instantaneity of the detection but to the temporal accuracy thereof.
From a mathematical point of view, the time of arrival of a signal, for example step- or pulse-wise, may be defined as the instant at which the leading edge thereof crosses a threshold depending on the maximum amplitude of the signal itself, where the threshold may be defined in linear scale or in logarithmic scale. Typically, a level is chosen as a threshold whereat the time derivative of the signal is high, or even maximum, in order to facilitate the detection.
For example, it is often chosen as threshold level a level corresponding to 50% of the maximum signal amplitude, in linear notation, which in logarithmic notation corresponds to a level set at −6 dB relative to the maximum peak reached.
In the above-mentioned example, if the maximum signal amplitude is not known in advance, it is not possible to instantaneously determine the threshold crossing; in this case a sort of signal recording is required, in analog or digital form, which allows evaluating the amplitude thereof, and thus calculating the threshold (in this example corresponding to 50% of the amplitude), determining the instant at which the signal crosses such threshold and emitting a detection signal of a time of arrival, having a fixed and known delay relative to the time of arrival.
Thus, in such example, a known method for determining the time of arrival of the signal consists in detecting the signal peak (that is, the maximum amplitude reached), dividing such peak by two (that is, attenuating it by 6 dB) for generating a constant halved peak signal, and comparing such constant halved peak signal with the original signal delayed by a delay T0, at least equal to the time taken by the signal for rising from 50% to 100% of its peak level.
The first crossing between the halved peak signal and the original delayed signal takes place at 50% (that is, at −6 dB) of the peak level of the original delayed signal. A detection signal, or “trigger”, of the time of arrival is generated at the instant at which such crossing takes place, wherein the trigger is synchronized with the time of arrival, with a delay equal to delay T0 imposed to the signal.
The method described above may be implemented by analog electronics. In this case, however, the detection accuracy of the time of arrival is related to noise and thermal drift features of the analog circuits that are used.
The analog detection method, actually, is less and less used, because of the accuracy limitations due to the reasons mentioned above. Moreover, the analog nature of such method does not allow having numerical results and outcomes and therefore it cannot be used in the field of digital electronics, nowadays prevailing.
For this reason, the state of the art envisages that the same functional method for determining the time of arrival, described above, is converted in a mathematical algorithm implementable through a digital circuitry, which in particular may be an FPGA (Field Programmable Gate Array) circuitry. To this end, the input signal is acquired with an analog-digital converter (ADC), and all the following process is performed through numerical calculations.
Let's thus consider said digital methods for detecting the time of arrival, or more in general, for detecting a threshold crossing instant by an electrical signal.
Due to their digital nature, said methods intrinsically exhibit a temporal discretization which limits the accuracy that may be obtained in the detection.
In fact the resolution, and thus the accuracy, with which the threshold crossing instant is determined, is subordinated to the selection of the system clock, which is actually constrained by strict design requirements for the electronic device that implements the method. Ideally, a clock operating at very high frequencies (thus with a very short clock period) would ensure a good resolution but would give rise to a circuit complexity, to signal integrity problems, to energy consumptions and to costs not compatible with realistic solutions.
On the other hand, the use of clocks with cost and complexity compatible with the scope considered (for example, having a clock period in the order of 10 ns) limits the temporal resolution of the detection of the threshold crossing instant: the order of magnitude of such resolution is comparable to the clock period. As a consequence, the detection error margin, comparable to the clock period, may be unsatisfactory for many applications, such as the already mentioned reception and transmission systems for radars or for GPS localizers.